To implement Depth-First Search (DFS), Uniform-Cost Search (UCS), Best-First Search (BFS), and A* Algorithm to solve the following problems (i.e. find the goal): 1) 8 Puzzle Problem: The 8 puzzle consists of eight numbered, movable tiles set in a 3x3 frame. One cell of the frame is always empty thus making it possible to move an adjacent numbered tile into the empty cell. Start with a random state (cannot be fixed). The goal state is listed below. 1 2 3 8 4 765 The program is to change the initial configuration into the goal configuration. A solution to the problem is an appropriate sequence of moves. You must write your own codes for the algorithms. Make sure your submission meets all of the requirements and free of plagiarism. Your program should be able to address any initial configuration and provide a table of statistics below in your PDF file. Algorithm DFS BFS UCS A* Heuristics used in UCS Average number of nodes Average Run time Your comment on these visited (you need repeat each (Actual run time in algorithms algorithm several times with your program) different initial configuration)

When an author produces an index for his or her book, the first step in this process is to decide which words should go into the index; the second is to produce a list of the pages where each word occurs. Instead of trying to choose words out of our heads, we decided to let the computer produce a list of all the unique words used in the manuscript and their frequency of occurrence. We could then go over the list and choose which words to put into the index. The main object in this problem is a "word" with associated frequency. The tentative definition of "word" here is a string of alphanumeric characters between markers where markers are white space and all punctuation marks; anything non-alphanumeric stops the reading. If we skip all un-allowed characters before getting the string, we should have exactly what we want. Ignoring words of fewer than three letters will remove from consideration such as "a", "is", "to", "do", and "by" that do not belong in an index. In this project, you…

In python, Problem Description:You are hosting a party and do not have room to invite all of your friends. You use the following unemotional mathematical method to determine which friends to invite. Number your friends 1, 2, . . . , K and place them in a list in this order. Then perform m rounds. In each round, use a number to determine which friends to remove from the ordered list. The rounds will use numbers r1, r2, . . . , rm. In round i remove all the remaining people in positions that are multiples of ri (that is, ri, 2ri, 3ri, . . .) The beginning of the list is position 1. Output the numbers of the friends that remain after this removal process. Input Specification:The first line of input contains the integer K (1 ≤ K ≤ 100). The second line of input contains the integer m (1 ≤ m ≤ 10), which is the number of rounds of removal. The next m lines each contain one integer. The ith of these lines (1 ≤ i ≤ m) contains ri ( 2 ≤ ri ≤ 100) indicating that every person at a position…

How will this project be solved in Python? Thanks. There are example outputs in the picture.